1 Data preparation

1.1 Outline

  • Load scripts: loads libraries and useful scripts used in the analyses; all .R files contained in scripts at the root of the factory are automatically loaded

  • Load data: imports datasets, and may contain some ad hoc changes to the data such as specific data cleaning (not used in other reports), new variables used in the analyses, etc.

1.2 Load packages


library(reportfactory)
library(here)
library(rio) 
library(tidyverse)
library(incidence)
library(distcrete)
library(epitrix)
library(earlyR)
library(projections)
library(linelist)
library(remotes)
library(janitor)
library(kableExtra)
library(DT)
library(cyphr)
library(chngpt)
library(lubridate)
library(ggpubr)
library(ggnewscale)

1.3 Load scripts

These scripts will load:

  • all scripts stored as .R files inside /scripts/
  • all scripts stored as .R files inside /src/

These scripts also contain routines to access the latest clean encrypted data (see next section).


reportfactory::rfh_load_scripts()

1.4 Load clean data

We import the latest NHS pathways data:


x <- import_pathways() %>%
  as_tibble()
x
## # A tibble: 164,924 x 11
##    site_type date       sex   age   ccg_code ccg_name count postcode nhs_region
##    <chr>     <date>     <chr> <chr> <chr>    <chr>    <int> <chr>    <chr>     
##  1 111       2020-03-18 fema… miss… e380000… nhs_glo…     1 gl34fe   South West
##  2 111       2020-03-18 fema… miss… e380001… nhs_sou…     1 ne325nn  North Eas…
##  3 111       2020-03-18 fema… 0-18  e380000… nhs_air…     8 bd57jr   North Eas…
##  4 111       2020-03-18 fema… 0-18  e380000… nhs_ash…     7 tn254ab  South East
##  5 111       2020-03-18 fema… 0-18  e380000… nhs_bar…    35 rm13ae   London    
##  6 111       2020-03-18 fema… 0-18  e380000… nhs_bar…     9 n111np   London    
##  7 111       2020-03-18 fema… 0-18  e380000… nhs_bar…    11 s752py   North Eas…
##  8 111       2020-03-18 fema… 0-18  e380000… nhs_bas…    19 ss143hg  East of E…
##  9 111       2020-03-18 fema… 0-18  e380000… nhs_bas…     6 dn227xf  North Eas…
## 10 111       2020-03-18 fema… 0-18  e380000… nhs_bat…     9 ba25rp   South West
## # … with 164,914 more rows, and 2 more variables: day <int>, weekday <fct>

We also import demographics data for NHS regions in England, used later in our analysis:


path <- here::here("data", "csv", "nhs_region_population_2018.csv")
nhs_region_pop <- rio::import(path) %>%
  mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))

nhs_region_pop$nhs_region <- gsub(" Of ", " of ", nhs_region_pop$nhs_region)
nhs_region_pop$nhs_region <- gsub(" And ", " and ", nhs_region_pop$nhs_region)
nhs_region_pop
##                  nhs_region variable      value
## 1                North West     0-18 0.22538599
## 2  North East and Yorkshire     0-18 0.21876449
## 3                  Midlands     0-18 0.22564656
## 4           East of England     0-18 0.22810783
## 5                    London     0-18 0.23764782
## 6                South East     0-18 0.22458811
## 7                South West     0-18 0.20799797
## 8                North West    19-69 0.64274078
## 9  North East and Yorkshire    19-69 0.64437753
## 10                 Midlands    19-69 0.63876675
## 11          East of England    19-69 0.63034229
## 12                   London    19-69 0.67820084
## 13               South East    19-69 0.63267336
## 14               South West    19-69 0.63176131
## 15               North West   70-120 0.13187323
## 16 North East and Yorkshire   70-120 0.13685797
## 17                 Midlands   70-120 0.13558669
## 18          East of England   70-120 0.14154988
## 19                   London   70-120 0.08415135
## 20               South East   70-120 0.14273853
## 21               South West   70-120 0.16024072

Finally, we import publically available deaths per NHS region:


dth <- import_deaths() %>%
  mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))

#truncation to account for reporting delay
delay_max <- 21

dth$nhs_region <- gsub(" Of ", " of ", dth$nhs_region)
dth$nhs_region <- gsub(" And ", " and ", dth$nhs_region)
dth
##     date_report               nhs_region deaths
## 1    2020-03-01          East of England      0
## 2    2020-03-02          East of England      1
## 3    2020-03-03          East of England      0
## 4    2020-03-04          East of England      0
## 5    2020-03-05          East of England      0
## 6    2020-03-06          East of England      1
## 7    2020-03-07          East of England      0
## 8    2020-03-08          East of England      0
## 9    2020-03-09          East of England      1
## 10   2020-03-10          East of England      0
## 11   2020-03-11          East of England      0
## 12   2020-03-12          East of England      0
## 13   2020-03-13          East of England      1
## 14   2020-03-14          East of England      2
## 15   2020-03-15          East of England      2
## 16   2020-03-16          East of England      1
## 17   2020-03-17          East of England      1
## 18   2020-03-18          East of England      5
## 19   2020-03-19          East of England      4
## 20   2020-03-20          East of England      2
## 21   2020-03-21          East of England     11
## 22   2020-03-22          East of England     12
## 23   2020-03-23          East of England     11
## 24   2020-03-24          East of England     19
## 25   2020-03-25          East of England     26
## 26   2020-03-26          East of England     36
## 27   2020-03-27          East of England     38
## 28   2020-03-28          East of England     28
## 29   2020-03-29          East of England     43
## 30   2020-03-30          East of England     45
## 31   2020-03-31          East of England     70
## 32   2020-04-01          East of England     62
## 33   2020-04-02          East of England     64
## 34   2020-04-03          East of England     80
## 35   2020-04-04          East of England     71
## 36   2020-04-05          East of England     76
## 37   2020-04-06          East of England     71
## 38   2020-04-07          East of England     93
## 39   2020-04-08          East of England    111
## 40   2020-04-09          East of England     87
## 41   2020-04-10          East of England     74
## 42   2020-04-11          East of England     92
## 43   2020-04-12          East of England    101
## 44   2020-04-13          East of England     78
## 45   2020-04-14          East of England     61
## 46   2020-04-15          East of England     82
## 47   2020-04-16          East of England     74
## 48   2020-04-17          East of England     86
## 49   2020-04-18          East of England     64
## 50   2020-04-19          East of England     67
## 51   2020-04-20          East of England     67
## 52   2020-04-21          East of England     75
## 53   2020-04-22          East of England     67
## 54   2020-04-23          East of England     49
## 55   2020-04-24          East of England     66
## 56   2020-04-25          East of England     54
## 57   2020-04-26          East of England     48
## 58   2020-04-27          East of England     46
## 59   2020-04-28          East of England     58
## 60   2020-04-29          East of England     32
## 61   2020-04-30          East of England     45
## 62   2020-05-01          East of England     49
## 63   2020-05-02          East of England     29
## 64   2020-05-03          East of England     41
## 65   2020-05-04          East of England     19
## 66   2020-05-05          East of England     36
## 67   2020-05-06          East of England     31
## 68   2020-05-07          East of England     33
## 69   2020-05-08          East of England     33
## 70   2020-05-09          East of England     29
## 71   2020-05-10          East of England     22
## 72   2020-05-11          East of England     18
## 73   2020-05-12          East of England     21
## 74   2020-05-13          East of England     27
## 75   2020-05-14          East of England     26
## 76   2020-05-15          East of England     19
## 77   2020-05-16          East of England     26
## 78   2020-05-17          East of England     17
## 79   2020-05-18          East of England     25
## 80   2020-05-19          East of England     15
## 81   2020-05-20          East of England     26
## 82   2020-05-21          East of England     21
## 83   2020-05-22          East of England     13
## 84   2020-05-23          East of England     12
## 85   2020-05-24          East of England     17
## 86   2020-05-25          East of England     25
## 87   2020-05-26          East of England     14
## 88   2020-05-27          East of England     12
## 89   2020-05-28          East of England     17
## 90   2020-05-29          East of England     16
## 91   2020-05-30          East of England      9
## 92   2020-05-31          East of England      8
## 93   2020-06-01          East of England     17
## 94   2020-06-02          East of England     14
## 95   2020-06-03          East of England     10
## 96   2020-06-04          East of England      7
## 97   2020-06-05          East of England     14
## 98   2020-06-06          East of England      5
## 99   2020-06-07          East of England      9
## 100  2020-06-08          East of England      7
## 101  2020-06-09          East of England      6
## 102  2020-06-10          East of England      8
## 103  2020-06-11          East of England      1
## 104  2020-06-12          East of England      9
## 105  2020-06-13          East of England      5
## 106  2020-06-14          East of England      4
## 107  2020-06-15          East of England      8
## 108  2020-06-16          East of England      3
## 109  2020-06-17          East of England      7
## 110  2020-06-18          East of England      4
## 111  2020-06-19          East of England      7
## 112  2020-06-20          East of England      4
## 113  2020-06-21          East of England      3
## 114  2020-06-22          East of England      6
## 115  2020-06-23          East of England      4
## 116  2020-06-24          East of England      4
## 117  2020-06-25          East of England      1
## 118  2020-06-26          East of England      5
## 119  2020-06-27          East of England      5
## 120  2020-06-28          East of England      7
## 121  2020-06-29          East of England      4
## 122  2020-06-30          East of England      1
## 123  2020-07-01          East of England      2
## 124  2020-07-02          East of England      0
## 125  2020-03-01                   London      0
## 126  2020-03-02                   London      0
## 127  2020-03-03                   London      0
## 128  2020-03-04                   London      0
## 129  2020-03-05                   London      0
## 130  2020-03-06                   London      1
## 131  2020-03-07                   London      0
## 132  2020-03-08                   London      0
## 133  2020-03-09                   London      1
## 134  2020-03-10                   London      0
## 135  2020-03-11                   London      6
## 136  2020-03-12                   London      6
## 137  2020-03-13                   London     10
## 138  2020-03-14                   London     14
## 139  2020-03-15                   London     10
## 140  2020-03-16                   London     15
## 141  2020-03-17                   London     23
## 142  2020-03-18                   London     27
## 143  2020-03-19                   London     25
## 144  2020-03-20                   London     44
## 145  2020-03-21                   London     49
## 146  2020-03-22                   London     54
## 147  2020-03-23                   London     63
## 148  2020-03-24                   London     87
## 149  2020-03-25                   London    113
## 150  2020-03-26                   London    129
## 151  2020-03-27                   London    130
## 152  2020-03-28                   London    122
## 153  2020-03-29                   London    146
## 154  2020-03-30                   London    149
## 155  2020-03-31                   London    181
## 156  2020-04-01                   London    202
## 157  2020-04-02                   London    191
## 158  2020-04-03                   London    196
## 159  2020-04-04                   London    230
## 160  2020-04-05                   London    195
## 161  2020-04-06                   London    197
## 162  2020-04-07                   London    220
## 163  2020-04-08                   London    238
## 164  2020-04-09                   London    206
## 165  2020-04-10                   London    170
## 166  2020-04-11                   London    178
## 167  2020-04-12                   London    158
## 168  2020-04-13                   London    166
## 169  2020-04-14                   London    144
## 170  2020-04-15                   London    142
## 171  2020-04-16                   London    140
## 172  2020-04-17                   London    100
## 173  2020-04-18                   London    101
## 174  2020-04-19                   London    103
## 175  2020-04-20                   London     95
## 176  2020-04-21                   London     94
## 177  2020-04-22                   London    109
## 178  2020-04-23                   London     77
## 179  2020-04-24                   London     71
## 180  2020-04-25                   London     58
## 181  2020-04-26                   London     53
## 182  2020-04-27                   London     51
## 183  2020-04-28                   London     44
## 184  2020-04-29                   London     44
## 185  2020-04-30                   London     40
## 186  2020-05-01                   London     41
## 187  2020-05-02                   London     41
## 188  2020-05-03                   London     36
## 189  2020-05-04                   London     30
## 190  2020-05-05                   London     25
## 191  2020-05-06                   London     37
## 192  2020-05-07                   London     37
## 193  2020-05-08                   London     30
## 194  2020-05-09                   London     23
## 195  2020-05-10                   London     26
## 196  2020-05-11                   London     18
## 197  2020-05-12                   London     18
## 198  2020-05-13                   London     17
## 199  2020-05-14                   London     20
## 200  2020-05-15                   London     18
## 201  2020-05-16                   London     14
## 202  2020-05-17                   London     15
## 203  2020-05-18                   London      9
## 204  2020-05-19                   London     14
## 205  2020-05-20                   London     19
## 206  2020-05-21                   London     12
## 207  2020-05-22                   London     10
## 208  2020-05-23                   London      6
## 209  2020-05-24                   London      7
## 210  2020-05-25                   London      9
## 211  2020-05-26                   London     13
## 212  2020-05-27                   London      7
## 213  2020-05-28                   London      8
## 214  2020-05-29                   London      7
## 215  2020-05-30                   London     12
## 216  2020-05-31                   London      6
## 217  2020-06-01                   London     10
## 218  2020-06-02                   London      7
## 219  2020-06-03                   London      6
## 220  2020-06-04                   London      8
## 221  2020-06-05                   London      4
## 222  2020-06-06                   London      0
## 223  2020-06-07                   London      5
## 224  2020-06-08                   London      5
## 225  2020-06-09                   London      4
## 226  2020-06-10                   London      7
## 227  2020-06-11                   London      5
## 228  2020-06-12                   London      3
## 229  2020-06-13                   London      3
## 230  2020-06-14                   London      3
## 231  2020-06-15                   London      1
## 232  2020-06-16                   London      2
## 233  2020-06-17                   London      1
## 234  2020-06-18                   London      2
## 235  2020-06-19                   London      3
## 236  2020-06-20                   London      3
## 237  2020-06-21                   London      4
## 238  2020-06-22                   London      2
## 239  2020-06-23                   London      0
## 240  2020-06-24                   London      4
## 241  2020-06-25                   London      3
## 242  2020-06-26                   London      2
## 243  2020-06-27                   London      1
## 244  2020-06-28                   London      1
## 245  2020-06-29                   London      2
## 246  2020-06-30                   London      1
## 247  2020-07-01                   London      0
## 248  2020-07-02                   London      1
## 249  2020-03-01                 Midlands      0
## 250  2020-03-02                 Midlands      0
## 251  2020-03-03                 Midlands      1
## 252  2020-03-04                 Midlands      0
## 253  2020-03-05                 Midlands      0
## 254  2020-03-06                 Midlands      0
## 255  2020-03-07                 Midlands      0
## 256  2020-03-08                 Midlands      3
## 257  2020-03-09                 Midlands      1
## 258  2020-03-10                 Midlands      0
## 259  2020-03-11                 Midlands      2
## 260  2020-03-12                 Midlands      6
## 261  2020-03-13                 Midlands      5
## 262  2020-03-14                 Midlands      4
## 263  2020-03-15                 Midlands      5
## 264  2020-03-16                 Midlands     11
## 265  2020-03-17                 Midlands      8
## 266  2020-03-18                 Midlands     13
## 267  2020-03-19                 Midlands      8
## 268  2020-03-20                 Midlands     28
## 269  2020-03-21                 Midlands     13
## 270  2020-03-22                 Midlands     31
## 271  2020-03-23                 Midlands     33
## 272  2020-03-24                 Midlands     41
## 273  2020-03-25                 Midlands     48
## 274  2020-03-26                 Midlands     64
## 275  2020-03-27                 Midlands     72
## 276  2020-03-28                 Midlands     89
## 277  2020-03-29                 Midlands     92
## 278  2020-03-30                 Midlands     90
## 279  2020-03-31                 Midlands    123
## 280  2020-04-01                 Midlands    140
## 281  2020-04-02                 Midlands    142
## 282  2020-04-03                 Midlands    124
## 283  2020-04-04                 Midlands    151
## 284  2020-04-05                 Midlands    164
## 285  2020-04-06                 Midlands    140
## 286  2020-04-07                 Midlands    123
## 287  2020-04-08                 Midlands    186
## 288  2020-04-09                 Midlands    139
## 289  2020-04-10                 Midlands    127
## 290  2020-04-11                 Midlands    142
## 291  2020-04-12                 Midlands    139
## 292  2020-04-13                 Midlands    120
## 293  2020-04-14                 Midlands    116
## 294  2020-04-15                 Midlands    147
## 295  2020-04-16                 Midlands    102
## 296  2020-04-17                 Midlands    118
## 297  2020-04-18                 Midlands    115
## 298  2020-04-19                 Midlands     92
## 299  2020-04-20                 Midlands    107
## 300  2020-04-21                 Midlands     86
## 301  2020-04-22                 Midlands     78
## 302  2020-04-23                 Midlands    103
## 303  2020-04-24                 Midlands     79
## 304  2020-04-25                 Midlands     72
## 305  2020-04-26                 Midlands     81
## 306  2020-04-27                 Midlands     74
## 307  2020-04-28                 Midlands     68
## 308  2020-04-29                 Midlands     53
## 309  2020-04-30                 Midlands     56
## 310  2020-05-01                 Midlands     64
## 311  2020-05-02                 Midlands     51
## 312  2020-05-03                 Midlands     52
## 313  2020-05-04                 Midlands     61
## 314  2020-05-05                 Midlands     59
## 315  2020-05-06                 Midlands     59
## 316  2020-05-07                 Midlands     48
## 317  2020-05-08                 Midlands     34
## 318  2020-05-09                 Midlands     37
## 319  2020-05-10                 Midlands     42
## 320  2020-05-11                 Midlands     33
## 321  2020-05-12                 Midlands     45
## 322  2020-05-13                 Midlands     40
## 323  2020-05-14                 Midlands     37
## 324  2020-05-15                 Midlands     40
## 325  2020-05-16                 Midlands     34
## 326  2020-05-17                 Midlands     31
## 327  2020-05-18                 Midlands     34
## 328  2020-05-19                 Midlands     34
## 329  2020-05-20                 Midlands     36
## 330  2020-05-21                 Midlands     32
## 331  2020-05-22                 Midlands     27
## 332  2020-05-23                 Midlands     34
## 333  2020-05-24                 Midlands     19
## 334  2020-05-25                 Midlands     26
## 335  2020-05-26                 Midlands     33
## 336  2020-05-27                 Midlands     29
## 337  2020-05-28                 Midlands     28
## 338  2020-05-29                 Midlands     20
## 339  2020-05-30                 Midlands     20
## 340  2020-05-31                 Midlands     22
## 341  2020-06-01                 Midlands     20
## 342  2020-06-02                 Midlands     22
## 343  2020-06-03                 Midlands     24
## 344  2020-06-04                 Midlands     16
## 345  2020-06-05                 Midlands     21
## 346  2020-06-06                 Midlands     20
## 347  2020-06-07                 Midlands     17
## 348  2020-06-08                 Midlands     16
## 349  2020-06-09                 Midlands     18
## 350  2020-06-10                 Midlands     15
## 351  2020-06-11                 Midlands     13
## 352  2020-06-12                 Midlands     12
## 353  2020-06-13                 Midlands      6
## 354  2020-06-14                 Midlands     18
## 355  2020-06-15                 Midlands     12
## 356  2020-06-16                 Midlands     15
## 357  2020-06-17                 Midlands     10
## 358  2020-06-18                 Midlands     15
## 359  2020-06-19                 Midlands      9
## 360  2020-06-20                 Midlands     15
## 361  2020-06-21                 Midlands     13
## 362  2020-06-22                 Midlands     13
## 363  2020-06-23                 Midlands     17
## 364  2020-06-24                 Midlands     14
## 365  2020-06-25                 Midlands     17
## 366  2020-06-26                 Midlands      5
## 367  2020-06-27                 Midlands      4
## 368  2020-06-28                 Midlands      5
## 369  2020-06-29                 Midlands      5
## 370  2020-06-30                 Midlands      5
## 371  2020-07-01                 Midlands      2
## 372  2020-07-02                 Midlands      2
## 373  2020-03-01 North East and Yorkshire      0
## 374  2020-03-02 North East and Yorkshire      0
## 375  2020-03-03 North East and Yorkshire      0
## 376  2020-03-04 North East and Yorkshire      0
## 377  2020-03-05 North East and Yorkshire      0
## 378  2020-03-06 North East and Yorkshire      0
## 379  2020-03-07 North East and Yorkshire      0
## 380  2020-03-08 North East and Yorkshire      0
## 381  2020-03-09 North East and Yorkshire      0
## 382  2020-03-10 North East and Yorkshire      0
## 383  2020-03-11 North East and Yorkshire      0
## 384  2020-03-12 North East and Yorkshire      0
## 385  2020-03-13 North East and Yorkshire      0
## 386  2020-03-14 North East and Yorkshire      0
## 387  2020-03-15 North East and Yorkshire      2
## 388  2020-03-16 North East and Yorkshire      3
## 389  2020-03-17 North East and Yorkshire      1
## 390  2020-03-18 North East and Yorkshire      2
## 391  2020-03-19 North East and Yorkshire      6
## 392  2020-03-20 North East and Yorkshire      5
## 393  2020-03-21 North East and Yorkshire      6
## 394  2020-03-22 North East and Yorkshire      7
## 395  2020-03-23 North East and Yorkshire      9
## 396  2020-03-24 North East and Yorkshire      8
## 397  2020-03-25 North East and Yorkshire     18
## 398  2020-03-26 North East and Yorkshire     21
## 399  2020-03-27 North East and Yorkshire     28
## 400  2020-03-28 North East and Yorkshire     35
## 401  2020-03-29 North East and Yorkshire     38
## 402  2020-03-30 North East and Yorkshire     64
## 403  2020-03-31 North East and Yorkshire     60
## 404  2020-04-01 North East and Yorkshire     67
## 405  2020-04-02 North East and Yorkshire     75
## 406  2020-04-03 North East and Yorkshire    100
## 407  2020-04-04 North East and Yorkshire    105
## 408  2020-04-05 North East and Yorkshire     92
## 409  2020-04-06 North East and Yorkshire     96
## 410  2020-04-07 North East and Yorkshire    102
## 411  2020-04-08 North East and Yorkshire    107
## 412  2020-04-09 North East and Yorkshire    111
## 413  2020-04-10 North East and Yorkshire    117
## 414  2020-04-11 North East and Yorkshire     98
## 415  2020-04-12 North East and Yorkshire     84
## 416  2020-04-13 North East and Yorkshire     94
## 417  2020-04-14 North East and Yorkshire    107
## 418  2020-04-15 North East and Yorkshire     96
## 419  2020-04-16 North East and Yorkshire    103
## 420  2020-04-17 North East and Yorkshire     88
## 421  2020-04-18 North East and Yorkshire     95
## 422  2020-04-19 North East and Yorkshire     88
## 423  2020-04-20 North East and Yorkshire    100
## 424  2020-04-21 North East and Yorkshire     76
## 425  2020-04-22 North East and Yorkshire     84
## 426  2020-04-23 North East and Yorkshire     63
## 427  2020-04-24 North East and Yorkshire     72
## 428  2020-04-25 North East and Yorkshire     69
## 429  2020-04-26 North East and Yorkshire     65
## 430  2020-04-27 North East and Yorkshire     65
## 431  2020-04-28 North East and Yorkshire     57
## 432  2020-04-29 North East and Yorkshire     69
## 433  2020-04-30 North East and Yorkshire     57
## 434  2020-05-01 North East and Yorkshire     64
## 435  2020-05-02 North East and Yorkshire     48
## 436  2020-05-03 North East and Yorkshire     40
## 437  2020-05-04 North East and Yorkshire     49
## 438  2020-05-05 North East and Yorkshire     40
## 439  2020-05-06 North East and Yorkshire     51
## 440  2020-05-07 North East and Yorkshire     45
## 441  2020-05-08 North East and Yorkshire     42
## 442  2020-05-09 North East and Yorkshire     44
## 443  2020-05-10 North East and Yorkshire     40
## 444  2020-05-11 North East and Yorkshire     29
## 445  2020-05-12 North East and Yorkshire     27
## 446  2020-05-13 North East and Yorkshire     28
## 447  2020-05-14 North East and Yorkshire     31
## 448  2020-05-15 North East and Yorkshire     32
## 449  2020-05-16 North East and Yorkshire     35
## 450  2020-05-17 North East and Yorkshire     26
## 451  2020-05-18 North East and Yorkshire     30
## 452  2020-05-19 North East and Yorkshire     27
## 453  2020-05-20 North East and Yorkshire     22
## 454  2020-05-21 North East and Yorkshire     33
## 455  2020-05-22 North East and Yorkshire     22
## 456  2020-05-23 North East and Yorkshire     18
## 457  2020-05-24 North East and Yorkshire     26
## 458  2020-05-25 North East and Yorkshire     21
## 459  2020-05-26 North East and Yorkshire     21
## 460  2020-05-27 North East and Yorkshire     22
## 461  2020-05-28 North East and Yorkshire     21
## 462  2020-05-29 North East and Yorkshire     25
## 463  2020-05-30 North East and Yorkshire     20
## 464  2020-05-31 North East and Yorkshire     20
## 465  2020-06-01 North East and Yorkshire     17
## 466  2020-06-02 North East and Yorkshire     23
## 467  2020-06-03 North East and Yorkshire     23
## 468  2020-06-04 North East and Yorkshire     17
## 469  2020-06-05 North East and Yorkshire     18
## 470  2020-06-06 North East and Yorkshire     21
## 471  2020-06-07 North East and Yorkshire     14
## 472  2020-06-08 North East and Yorkshire     11
## 473  2020-06-09 North East and Yorkshire     12
## 474  2020-06-10 North East and Yorkshire     18
## 475  2020-06-11 North East and Yorkshire      7
## 476  2020-06-12 North East and Yorkshire      9
## 477  2020-06-13 North East and Yorkshire     10
## 478  2020-06-14 North East and Yorkshire     11
## 479  2020-06-15 North East and Yorkshire      9
## 480  2020-06-16 North East and Yorkshire     10
## 481  2020-06-17 North East and Yorkshire      9
## 482  2020-06-18 North East and Yorkshire     10
## 483  2020-06-19 North East and Yorkshire      6
## 484  2020-06-20 North East and Yorkshire      4
## 485  2020-06-21 North East and Yorkshire      4
## 486  2020-06-22 North East and Yorkshire      6
## 487  2020-06-23 North East and Yorkshire      7
## 488  2020-06-24 North East and Yorkshire     10
## 489  2020-06-25 North East and Yorkshire      3
## 490  2020-06-26 North East and Yorkshire      7
## 491  2020-06-27 North East and Yorkshire      3
## 492  2020-06-28 North East and Yorkshire      4
## 493  2020-06-29 North East and Yorkshire      2
## 494  2020-06-30 North East and Yorkshire      4
## 495  2020-07-01 North East and Yorkshire      1
## 496  2020-07-02 North East and Yorkshire      1
## 497  2020-03-01               North West      0
## 498  2020-03-02               North West      0
## 499  2020-03-03               North West      0
## 500  2020-03-04               North West      0
## 501  2020-03-05               North West      1
## 502  2020-03-06               North West      0
## 503  2020-03-07               North West      0
## 504  2020-03-08               North West      1
## 505  2020-03-09               North West      0
## 506  2020-03-10               North West      0
## 507  2020-03-11               North West      0
## 508  2020-03-12               North West      2
## 509  2020-03-13               North West      3
## 510  2020-03-14               North West      1
## 511  2020-03-15               North West      4
## 512  2020-03-16               North West      2
## 513  2020-03-17               North West      4
## 514  2020-03-18               North West      6
## 515  2020-03-19               North West      7
## 516  2020-03-20               North West     10
## 517  2020-03-21               North West     11
## 518  2020-03-22               North West     13
## 519  2020-03-23               North West     15
## 520  2020-03-24               North West     21
## 521  2020-03-25               North West     21
## 522  2020-03-26               North West     29
## 523  2020-03-27               North West     36
## 524  2020-03-28               North West     28
## 525  2020-03-29               North West     46
## 526  2020-03-30               North West     67
## 527  2020-03-31               North West     52
## 528  2020-04-01               North West     86
## 529  2020-04-02               North West     96
## 530  2020-04-03               North West     95
## 531  2020-04-04               North West     98
## 532  2020-04-05               North West    102
## 533  2020-04-06               North West    100
## 534  2020-04-07               North West    135
## 535  2020-04-08               North West    127
## 536  2020-04-09               North West    119
## 537  2020-04-10               North West    117
## 538  2020-04-11               North West    138
## 539  2020-04-12               North West    125
## 540  2020-04-13               North West    129
## 541  2020-04-14               North West    131
## 542  2020-04-15               North West    114
## 543  2020-04-16               North West    135
## 544  2020-04-17               North West     98
## 545  2020-04-18               North West    113
## 546  2020-04-19               North West     71
## 547  2020-04-20               North West     83
## 548  2020-04-21               North West     76
## 549  2020-04-22               North West     86
## 550  2020-04-23               North West     85
## 551  2020-04-24               North West     66
## 552  2020-04-25               North West     66
## 553  2020-04-26               North West     55
## 554  2020-04-27               North West     54
## 555  2020-04-28               North West     57
## 556  2020-04-29               North West     63
## 557  2020-04-30               North West     59
## 558  2020-05-01               North West     45
## 559  2020-05-02               North West     56
## 560  2020-05-03               North West     55
## 561  2020-05-04               North West     48
## 562  2020-05-05               North West     48
## 563  2020-05-06               North West     44
## 564  2020-05-07               North West     49
## 565  2020-05-08               North West     42
## 566  2020-05-09               North West     30
## 567  2020-05-10               North West     41
## 568  2020-05-11               North West     35
## 569  2020-05-12               North West     38
## 570  2020-05-13               North West     25
## 571  2020-05-14               North West     26
## 572  2020-05-15               North West     33
## 573  2020-05-16               North West     32
## 574  2020-05-17               North West     24
## 575  2020-05-18               North West     31
## 576  2020-05-19               North West     35
## 577  2020-05-20               North West     27
## 578  2020-05-21               North West     27
## 579  2020-05-22               North West     26
## 580  2020-05-23               North West     31
## 581  2020-05-24               North West     26
## 582  2020-05-25               North West     31
## 583  2020-05-26               North West     27
## 584  2020-05-27               North West     27
## 585  2020-05-28               North West     28
## 586  2020-05-29               North West     20
## 587  2020-05-30               North West     19
## 588  2020-05-31               North West     13
## 589  2020-06-01               North West     12
## 590  2020-06-02               North West     27
## 591  2020-06-03               North West     22
## 592  2020-06-04               North West     22
## 593  2020-06-05               North West     16
## 594  2020-06-06               North West     26
## 595  2020-06-07               North West     20
## 596  2020-06-08               North West     23
## 597  2020-06-09               North West     17
## 598  2020-06-10               North West     16
## 599  2020-06-11               North West     16
## 600  2020-06-12               North West     11
## 601  2020-06-13               North West     10
## 602  2020-06-14               North West     15
## 603  2020-06-15               North West     15
## 604  2020-06-16               North West     13
## 605  2020-06-17               North West     12
## 606  2020-06-18               North West     13
## 607  2020-06-19               North West      7
## 608  2020-06-20               North West     11
## 609  2020-06-21               North West      6
## 610  2020-06-22               North West     11
## 611  2020-06-23               North West     13
## 612  2020-06-24               North West     13
## 613  2020-06-25               North West     14
## 614  2020-06-26               North West      4
## 615  2020-06-27               North West      6
## 616  2020-06-28               North West      8
## 617  2020-06-29               North West      4
## 618  2020-06-30               North West      5
## 619  2020-07-01               North West      2
## 620  2020-07-02               North West      2
## 621  2020-03-01               South East      0
## 622  2020-03-02               South East      0
## 623  2020-03-03               South East      1
## 624  2020-03-04               South East      0
## 625  2020-03-05               South East      1
## 626  2020-03-06               South East      0
## 627  2020-03-07               South East      0
## 628  2020-03-08               South East      1
## 629  2020-03-09               South East      1
## 630  2020-03-10               South East      1
## 631  2020-03-11               South East      1
## 632  2020-03-12               South East      0
## 633  2020-03-13               South East      1
## 634  2020-03-14               South East      1
## 635  2020-03-15               South East      5
## 636  2020-03-16               South East      8
## 637  2020-03-17               South East      7
## 638  2020-03-18               South East     10
## 639  2020-03-19               South East      9
## 640  2020-03-20               South East     13
## 641  2020-03-21               South East      7
## 642  2020-03-22               South East     25
## 643  2020-03-23               South East     20
## 644  2020-03-24               South East     22
## 645  2020-03-25               South East     29
## 646  2020-03-26               South East     35
## 647  2020-03-27               South East     34
## 648  2020-03-28               South East     36
## 649  2020-03-29               South East     55
## 650  2020-03-30               South East     58
## 651  2020-03-31               South East     65
## 652  2020-04-01               South East     66
## 653  2020-04-02               South East     55
## 654  2020-04-03               South East     72
## 655  2020-04-04               South East     80
## 656  2020-04-05               South East     82
## 657  2020-04-06               South East     88
## 658  2020-04-07               South East    100
## 659  2020-04-08               South East     83
## 660  2020-04-09               South East    104
## 661  2020-04-10               South East     88
## 662  2020-04-11               South East     88
## 663  2020-04-12               South East     88
## 664  2020-04-13               South East     84
## 665  2020-04-14               South East     65
## 666  2020-04-15               South East     72
## 667  2020-04-16               South East     56
## 668  2020-04-17               South East     86
## 669  2020-04-18               South East     57
## 670  2020-04-19               South East     70
## 671  2020-04-20               South East     87
## 672  2020-04-21               South East     51
## 673  2020-04-22               South East     54
## 674  2020-04-23               South East     57
## 675  2020-04-24               South East     64
## 676  2020-04-25               South East     51
## 677  2020-04-26               South East     51
## 678  2020-04-27               South East     40
## 679  2020-04-28               South East     40
## 680  2020-04-29               South East     47
## 681  2020-04-30               South East     29
## 682  2020-05-01               South East     37
## 683  2020-05-02               South East     36
## 684  2020-05-03               South East     17
## 685  2020-05-04               South East     35
## 686  2020-05-05               South East     29
## 687  2020-05-06               South East     25
## 688  2020-05-07               South East     27
## 689  2020-05-08               South East     26
## 690  2020-05-09               South East     28
## 691  2020-05-10               South East     19
## 692  2020-05-11               South East     25
## 693  2020-05-12               South East     27
## 694  2020-05-13               South East     18
## 695  2020-05-14               South East     32
## 696  2020-05-15               South East     24
## 697  2020-05-16               South East     22
## 698  2020-05-17               South East     18
## 699  2020-05-18               South East     22
## 700  2020-05-19               South East     12
## 701  2020-05-20               South East     22
## 702  2020-05-21               South East     15
## 703  2020-05-22               South East     17
## 704  2020-05-23               South East     21
## 705  2020-05-24               South East     17
## 706  2020-05-25               South East     13
## 707  2020-05-26               South East     19
## 708  2020-05-27               South East     18
## 709  2020-05-28               South East     12
## 710  2020-05-29               South East     21
## 711  2020-05-30               South East      8
## 712  2020-05-31               South East     12
## 713  2020-06-01               South East     11
## 714  2020-06-02               South East     13
## 715  2020-06-03               South East     18
## 716  2020-06-04               South East     11
## 717  2020-06-05               South East     11
## 718  2020-06-06               South East     10
## 719  2020-06-07               South East     12
## 720  2020-06-08               South East      8
## 721  2020-06-09               South East     10
## 722  2020-06-10               South East     11
## 723  2020-06-11               South East      5
## 724  2020-06-12               South East      6
## 725  2020-06-13               South East      6
## 726  2020-06-14               South East      7
## 727  2020-06-15               South East      8
## 728  2020-06-16               South East     12
## 729  2020-06-17               South East      9
## 730  2020-06-18               South East      4
## 731  2020-06-19               South East      6
## 732  2020-06-20               South East      5
## 733  2020-06-21               South East      3
## 734  2020-06-22               South East      2
## 735  2020-06-23               South East      8
## 736  2020-06-24               South East      6
## 737  2020-06-25               South East      4
## 738  2020-06-26               South East      7
## 739  2020-06-27               South East      7
## 740  2020-06-28               South East      6
## 741  2020-06-29               South East      5
## 742  2020-06-30               South East      4
## 743  2020-07-01               South East      1
## 744  2020-07-02               South East      0
## 745  2020-03-01               South West      0
## 746  2020-03-02               South West      0
## 747  2020-03-03               South West      0
## 748  2020-03-04               South West      0
## 749  2020-03-05               South West      0
## 750  2020-03-06               South West      0
## 751  2020-03-07               South West      0
## 752  2020-03-08               South West      0
## 753  2020-03-09               South West      0
## 754  2020-03-10               South West      0
## 755  2020-03-11               South West      1
## 756  2020-03-12               South West      0
## 757  2020-03-13               South West      0
## 758  2020-03-14               South West      1
## 759  2020-03-15               South West      0
## 760  2020-03-16               South West      0
## 761  2020-03-17               South West      2
## 762  2020-03-18               South West      2
## 763  2020-03-19               South West      4
## 764  2020-03-20               South West      3
## 765  2020-03-21               South West      6
## 766  2020-03-22               South West      7
## 767  2020-03-23               South West      8
## 768  2020-03-24               South West      7
## 769  2020-03-25               South West      9
## 770  2020-03-26               South West     11
## 771  2020-03-27               South West     13
## 772  2020-03-28               South West     21
## 773  2020-03-29               South West     18
## 774  2020-03-30               South West     23
## 775  2020-03-31               South West     23
## 776  2020-04-01               South West     22
## 777  2020-04-02               South West     23
## 778  2020-04-03               South West     30
## 779  2020-04-04               South West     42
## 780  2020-04-05               South West     32
## 781  2020-04-06               South West     34
## 782  2020-04-07               South West     39
## 783  2020-04-08               South West     47
## 784  2020-04-09               South West     24
## 785  2020-04-10               South West     46
## 786  2020-04-11               South West     43
## 787  2020-04-12               South West     23
## 788  2020-04-13               South West     27
## 789  2020-04-14               South West     24
## 790  2020-04-15               South West     32
## 791  2020-04-16               South West     29
## 792  2020-04-17               South West     33
## 793  2020-04-18               South West     25
## 794  2020-04-19               South West     31
## 795  2020-04-20               South West     26
## 796  2020-04-21               South West     26
## 797  2020-04-22               South West     23
## 798  2020-04-23               South West     17
## 799  2020-04-24               South West     19
## 800  2020-04-25               South West     15
## 801  2020-04-26               South West     27
## 802  2020-04-27               South West     13
## 803  2020-04-28               South West     17
## 804  2020-04-29               South West     15
## 805  2020-04-30               South West     26
## 806  2020-05-01               South West      6
## 807  2020-05-02               South West      7
## 808  2020-05-03               South West     10
## 809  2020-05-04               South West     17
## 810  2020-05-05               South West     14
## 811  2020-05-06               South West     19
## 812  2020-05-07               South West     16
## 813  2020-05-08               South West      6
## 814  2020-05-09               South West     11
## 815  2020-05-10               South West      5
## 816  2020-05-11               South West      8
## 817  2020-05-12               South West      7
## 818  2020-05-13               South West      7
## 819  2020-05-14               South West      6
## 820  2020-05-15               South West      4
## 821  2020-05-16               South West      4
## 822  2020-05-17               South West      6
## 823  2020-05-18               South West      4
## 824  2020-05-19               South West      6
## 825  2020-05-20               South West      1
## 826  2020-05-21               South West      9
## 827  2020-05-22               South West      6
## 828  2020-05-23               South West      6
## 829  2020-05-24               South West      3
## 830  2020-05-25               South West      8
## 831  2020-05-26               South West     11
## 832  2020-05-27               South West      5
## 833  2020-05-28               South West     10
## 834  2020-05-29               South West      7
## 835  2020-05-30               South West      3
## 836  2020-05-31               South West      2
## 837  2020-06-01               South West      7
## 838  2020-06-02               South West      2
## 839  2020-06-03               South West      7
## 840  2020-06-04               South West      2
## 841  2020-06-05               South West      2
## 842  2020-06-06               South West      1
## 843  2020-06-07               South West      3
## 844  2020-06-08               South West      3
## 845  2020-06-09               South West      0
## 846  2020-06-10               South West      1
## 847  2020-06-11               South West      2
## 848  2020-06-12               South West      2
## 849  2020-06-13               South West      2
## 850  2020-06-14               South West      0
## 851  2020-06-15               South West      1
## 852  2020-06-16               South West      2
## 853  2020-06-17               South West      0
## 854  2020-06-18               South West      0
## 855  2020-06-19               South West      0
## 856  2020-06-20               South West      2
## 857  2020-06-21               South West      0
## 858  2020-06-22               South West      1
## 859  2020-06-23               South West      1
## 860  2020-06-24               South West      1
## 861  2020-06-25               South West      0
## 862  2020-06-26               South West      3
## 863  2020-06-27               South West      0
## 864  2020-06-28               South West      0
## 865  2020-06-29               South West      1
## 866  2020-06-30               South West      0
## 867  2020-07-01               South West      0
## 868  2020-07-02               South West      0

1.5 Completion date

We extract the completion date from the NHS Pathways file timestamp:


database_date <- attr(x, "timestamp")
database_date
## [1] "2020-07-02"

The completion date of the NHS Pathways data is Thursday 02 Jul 2020.

1.6 Auxiliary functions

These are functions which will be used further in the analyses.

Function to estimate the generalised R-squared as the proportion of deviance explained by a given model:


## Function to calculate R2 for Poisson model
## not adjusted for model complexity but all models have the same DF here

Rsq <- function(x) {
  1 - (x$deviance / x$null.deviance)
}

Function to extract growth rates per region as well as halving times, and the associated 95% confidence intervals:


## function to extract the coefficients, find the level of the intercept,
## reconstruct the values of r, get confidence intervals

get_r <- function(model) {
  ##  extract coefficients and conf int
  out <- data.frame(r = coef(model))  %>%
    rownames_to_column("var") %>% 
    cbind(confint(model)) %>%
    filter(!grepl("day_of_week", var)) %>% 
    filter(grepl("day", var)) %>%
    rename(lower_95 = "2.5 %",
           upper_95 = "97.5 %") %>%
    mutate(var = sub("day:", "", var))
  
  ## reconstruct values: intercept + region-coefficient
  for (i in 2:nrow(out)) {
    out[i, -1] <- out[1, -1] + out[i, -1]
  }
  
  ## find the name of the intercept, restore regions names
  out <- out %>%
    mutate(nhs_region = model$xlevels$nhs_region) %>%
    select(nhs_region, everything(), -var)
  
  ## find halving times
  halving <- log(0.5) / out[,-1] %>%
    rename(halving_t = r,
           halving_t_lower_95 = lower_95,
           halving_t_upper_95 = upper_95)
  
  ## set halving times with exclusion intervals to NA
  no_halving <- out$lower_95 < 0 & out$upper_95 > 0
  halving[no_halving, ] <- NA_real_
  
  ## return all data
  cbind(out, halving)
  
}

Functions used in the correlation analysis between NHS Pathways reports and deaths:

## Function to calculate Pearson's correlation between deaths and lagged
## reports. Note that `pearson` can be replaced with `spearman` for rank
## correlation.

getcor <- function(x, ndx) {
  return(cor(x$deaths[ndx],
             x$note_lag[ndx],
             use = "complete.obs",
             method = "pearson"))
}

## Catch if sample size throws an error
getcor2 <- possibly(getcor, otherwise = NA)

getboot <- function(x) {
  result <- boot::boot.ci(boot::boot(x, getcor2, R = 1000), 
                           type = "bca")
  return(data.frame(n = sum(!is.na(x$note_lag) & !is.na(x$deaths)),
                    r = result$t0,
                    r_low = result$bca[4],
                    r_hi = result$bca[5]))
}

Function to classify the day of the week into weekend, Monday, and the rest:


## Fn to add day of week
day_of_week <- function(df) {
  df %>% 
    dplyr::mutate(day_of_week = lubridate::wday(date, label = TRUE)) %>% 
    dplyr::mutate(day_of_week = dplyr::case_when(
      day_of_week %in% c("Sat", "Sun") ~ "weekend",
      day_of_week %in% c("Mon") ~ "monday",
      !(day_of_week %in% c("Sat", "Sun", "Mon")) ~ "rest_of_week"
    ) %>% 
      factor(levels = c("rest_of_week", "monday", "weekend")))
}

Custom color palettes, color scales, and vectors of colors:


pal <- c("#006212",
         "#ae3cab",
         "#00db90",
         "#960c00",
         "#55aaff",
         "#ff7e78",
         "#00388d")

age.pal <- viridis::viridis(3,begin = 0.1, end = 0.7)

3 Comparison with deaths time series

3.1 Outline

We want to explore the correlation between NHS Pathways reports and deaths, and assess the potential for reports to be used as an early warning system for disease resurgence.

Death data are publically available. We truncate the time series to avoid bias from reporting delay - we assume a conservative delay of three weeks.

3.2 Lagged correlation

We calculate Pearson’s correlation coefficient between deaths and NHS Pathways notifications using different lags. Confidence intervals are obtained using bootstrap. Note that results were also confirmed using Spearman’s rank correlation.

First we join the NHS Pathways and death data, and aggregate over all England:

## truncate death data for reporting delay
trunc_date <- max(dth$date_report) - delay_max

dth_trunc <- dth %>%
  rename(date = date_report) %>%
  filter(date <= trunc_date) 

## join with notification data
all_data <- x %>% 
  filter(!is.na(nhs_region)) %>%
  group_by(date, nhs_region) %>%
  summarise(count = sum(count, na.rm = T)) %>%
  ungroup %>%
  inner_join(dth_trunc,
             by = c("date","nhs_region"))

all_tot <- all_data %>%
  group_by(date) %>%
  summarise(count = sum(count, na.rm = TRUE),
            deaths = sum(deaths, na.rm = TRUE)) 

We calculate correlation with lagged NHS Pathways reports from 0 to 30 days behind deaths:


## Calculate all correlations + bootstrap CIs
lag_cor <- data.frame()
for (i in 0:30) {
  
  ## lag reports
  summary <- all_tot %>% 
    mutate(note_lag = lag(count, i)) %>%
    ## calculate rank correlation and bootstrap CI
    getboot(.) %>%
    mutate(lag = i)

  lag_cor <- bind_rows(lag_cor, summary)
}

cor_vs_lag <- ggplot(lag_cor, aes(lag, r)) +
  theme_bw() +
  geom_ribbon(aes(ymin = r_low, ymax = r_hi), alpha = 0.2) +
  geom_hline(yintercept = 0, lty = "longdash") +
  geom_point() +
  geom_line() +
  labs(x = "Lag between NHS pathways and death data (days)",
       y = "Pearson's correlation") +
  large_txt
cor_vs_lag


l_opt <- which.max(lag_cor$r)

This analysis suggests that the best lag is 23 days. We then compare and plot the number of deaths reported against the number of NHS Pathways reports lagged by 23 days.


all_tot <- all_tot %>%
  rename(date_death = date) %>%
  mutate(note_lag = lag(count, lag_cor$lag[l_opt]),
         note_lag_c = (note_lag - mean(note_lag, na.rm = T)),
         date_note = lag(date_death,16))

lag_mod <- glm(deaths ~ note_lag, data = all_tot, family = "quasipoisson")

summary(lag_mod)
## 
## Call:
## glm(formula = deaths ~ note_lag, family = "quasipoisson", data = all_tot)
## 
## Deviance Residuals: 
##      Min        1Q    Median        3Q       Max  
## -11.3458   -3.2936   -0.4328    3.4730    6.7003  
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 4.765e+00  5.858e-02   81.34   <2e-16 ***
## note_lag    1.312e-05  6.028e-07   21.77   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for quasipoisson family taken to be 17.1799)
## 
##     Null deviance: 8735.8  on 62  degrees of freedom
## Residual deviance: 1100.5  on 61  degrees of freedom
##   (23 observations deleted due to missingness)
## AIC: NA
## 
## Number of Fisher Scoring iterations: 4

exp(coefficients(lag_mod))
## (Intercept)    note_lag 
##  117.363079    1.000013
exp(confint(lag_mod))
##                  2.5 %     97.5 %
## (Intercept) 104.472098 131.447873
## note_lag      1.000012   1.000014

Rsq(lag_mod)
## [1] 0.8740239

mod_fit <- as.data.frame(predict(lag_mod, type = "link", se.fit = TRUE)[1:2])

all_tot_pred <- 
  all_tot %>%
  filter(!is.na(note_lag)) %>%
  mutate(pred = mod_fit$fit,
         pred.se = mod_fit$se.fit,
         low = exp(pred - 1.96*pred.se),
         hi = exp(pred + 1.96*pred.se))


glm_fit <- all_tot_pred %>% 
    filter(!is.na(note_lag)) %>%
  ggplot(aes(x = note_lag, y = deaths)) +
  geom_point() + 
  geom_line(aes(y = exp(pred))) + 
  geom_ribbon(aes(ymin = low, ymax = hi), alpha = 0.3, col = "grey") +
  theme_bw() +
  labs(y = "Daily number of\ndeaths reported",
       x = "Daily number of NHS Pathways reports") +
  large_txt

glm_fit

4 Supplementary figures

4.1 Serial interval distribution

This is a comparison of gamma versus lognormal distribution for the serial interval used to convert r to R in our analysis. Both distributions are parameterised with mean 4.7 and standard deviation 2.9.

SI_param <- epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale, w = 0.5)

SI_distribution2 <- distcrete::distcrete("lnorm", interval = 1,
                                        meanlog = log(4.7),
                                        sdlog = log(2.9), w = 0.5)

SI_dist1 <- data.frame(x = SI_distribution$r(1e5)) 
SI_dist1 <- count(SI_dist1, x) %>%
    ggplot() +
    geom_col(aes(x = x, y = n)) +
    labs(x = "Serial interval (days)", y = "Frequency") +
    scale_x_continuous(breaks = seq(0, 30, 5)) +
    theme_bw()

SI_dist2 <- data.frame(x = SI_distribution2$r(1e5)) 
SI_dist2 <- count(SI_dist2, x) %>%
    ggplot() +
    geom_col(aes(x = x, y = n)) +
    labs(x = "Serial interval (days)", y = "Frequency") +
    scale_x_continuous(breaks = seq(0, 200, 20), limits = c(0, 200)) +
    theme_bw()


ggpubr::ggarrange(SI_dist1,
                  SI_dist2,
                  nrow = 1,
                  labels = "AUTO") 

4.2 Sensitivity analysis - 7 or 21 days moving window

We reproduce the window analysis with either a 7 or 21 days window for sensitivity purposes.

First with the 7 days window:

## set moving time window (1/2/3 weeks)
w <- 7

# create empty df
r_all_sliding_7days <- NULL

## make data for model
x_model_all_moving <- x %>%
  filter(!is.na(nhs_region)) %>% 
  group_by(date, nhs_region) %>%
  summarise(n = sum(count)) 

unique_dates <- unique(x_model_all_moving$date)

for (i in 1:(length(unique_dates) - w)) {
  
  date_i <- unique_dates[i]
  
  date_i_max <- date_i + w
  
  model_data <- x_model_all_moving %>%
    filter(date >= date_i & date < date_i_max) %>%
    mutate(day = as.integer(date - date_i)) %>% 
    day_of_week()
  
  
  mod <- glm(n ~ day * nhs_region + day_of_week,
             data = model_data,
             family = 'quasipoisson')
  
  # get growth rate
  r <- get_r(mod)
  r$w_min <- date_i
  r$w_max <- date_i_max
  
  # combine all estimates
  r_all_sliding_7days <- bind_rows(r_all_sliding_7days, r)
  
}

#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale,
                                        w = 0.5)

#convert growth rates r to R0
r_all_sliding_7days <- r_all_sliding_7days %>%
  mutate(R = epitrix::r2R0(r, SI_distribution),
         R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
         R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))
# plot
plot_growth <-
  r_all_sliding_7days %>%
  ggplot(aes(x = w_max, y = r)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated daily growth rate (r)") +
  scale_colour_manual(values = pal)
plot_R <- r_all_sliding_7days %>%
  ggplot(aes(x = w_max, y = R)) +
  geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 1, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated effective reproduction\nnumber (Re)") +
  scale_colour_manual(values = pal)

R <- r_all_sliding_7days %>%
  mutate(lower_95 = R_lower_95, 
         upper_95 = R_upper_95,
         value = R,
         measure = "R",
         reference = 1)

r_R <- r_all_sliding_7days %>%
  mutate(measure = "r",
         value = r,
         reference = 0) %>%
  bind_rows(R)

r_R_7 <- r_R %>%
  ggplot(aes(x = w_max, y = value)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(aes(yintercept = reference), linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0,0, "cm"),
        strip.background = element_blank(),
        strip.placement = "outside"
  ) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "", y = "") +
  scale_colour_manual(values = pal) +
  facet_grid(rows = vars(measure),
             scales = "free_y",
             switch = "y",
             labeller = as_labeller(c(r = "Daily growth rate (r)",
                                      R = "Effective reproduction\nnumber (Re)")))

Then with the 21 days window:

## set moving time window (1/2/3 weeks)
w <- 21

# create empty df
r_all_sliding_21days <- NULL

## make data for model
x_model_all_moving <- x %>%
  filter(!is.na(nhs_region)) %>% 
  group_by(date, nhs_region) %>%
  summarise(n = sum(count)) 

unique_dates <- unique(x_model_all_moving$date)

for (i in 1:(length(unique_dates) - w)) {
  
  date_i <- unique_dates[i]
  
  date_i_max <- date_i + w
  
  model_data <- x_model_all_moving %>%
    filter(date >= date_i & date < date_i_max) %>%
    mutate(day = as.integer(date - date_i)) %>% 
    day_of_week()
  
  
  mod <- glm(n ~ day * nhs_region + day_of_week,
             data = model_data,
             family = 'quasipoisson')
  
  # get growth rate
  r <- get_r(mod)
  r$w_min <- date_i
  r$w_max <- date_i_max
  
  # combine all estimates
  r_all_sliding_21days <- bind_rows(r_all_sliding_21days, r)
  
}

#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale,
                                        w = 0.5)

#convert growth rates r to R0
r_all_sliding_21days <- r_all_sliding_21days %>%
  mutate(R = epitrix::r2R0(r, SI_distribution),
         R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
         R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))
# plot
plot_growth <-
  r_all_sliding_21days %>%
  ggplot(aes(x = w_max, y = r)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated daily growth rate (r)") +
  scale_colour_manual(values = pal)
# plot
plot_R <-
  r_all_sliding_21days %>%
  ggplot(aes(x = w_max, y = R)) +
  geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 1, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated effective reproduction\nnumber (Re)") +
  scale_colour_manual(values = pal)

R <- r_all_sliding_21days %>%
  mutate(lower_95 = R_lower_95, 
         upper_95 = R_upper_95,
         value = R,
         measure = "R",
         reference = 1)

r_R <- r_all_sliding_21days %>%
  mutate(measure = "r",
         value = r,
         reference = 0) %>%
  bind_rows(R)

r_R_21 <- r_R %>%
  ggplot(aes(x = w_max, y = value)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(aes(yintercept = reference), linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0,0, "cm"),
        strip.background = element_blank(),
        strip.placement = "outside"
  ) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "", y = "") +
  scale_colour_manual(values = pal) +
  facet_grid(rows = vars(measure),
             scales = "free_y",
             switch = "y",
             labeller = as_labeller(c(r = "Daily growth rate (r)",
                                      R = "Effective reproduction\nnumber (Re)")))

And we combine both outputs into a single plot:


ggpubr::ggarrange(r_R_7,
                  r_R_21,
                  nrow = 2,
                  labels = "AUTO",
                  common.legend = TRUE,
                  legend = "bottom") 

4.3 Correlation between NHS Pathways reports and deaths by NHS region


lag_cor_reg <- data.frame()

for (i in 0:30) {

  summary <-
    all_data %>%
    group_by(nhs_region) %>%
    mutate(note_lag = lag(count, i)) %>%
    ## calculate rank correlation and bootstrap CI for each region
    group_modify(~getboot(.x)) %>%
    mutate(lag = i)
  
  lag_cor_reg <- bind_rows(lag_cor_reg, summary)
}

cor_vs_lag_reg <- 
lag_cor_reg %>%
ggplot(aes(lag, r, col = nhs_region)) +
  geom_hline(yintercept = 0, lty = "longdash") +
  geom_ribbon(aes(ymin = r_low, ymax = r_hi, col = NULL, fill = nhs_region), alpha = 0.2) +
  geom_point() +
  geom_line() +
  facet_wrap(~nhs_region) +
  scale_color_manual(values = pal) +
  scale_fill_manual(values = pal, guide = F) +  
  theme_bw() +
  labs(x = "Lag between NHS pathways and death data (days)", y = "Pearson's correlation", col = "NHS region") +
  theme(legend.position = "bottom") +
  guides(color = guide_legend(override.aes = list(fill = NA)))

cor_vs_lag_reg

5 Export data

We save the tables created during our analysis:


if (!dir.exists("excel_tables")) {
  dir.create("excel_tables")
}


## list all tables, and loop over export
tables_to_export <- c("r_all_sliding", "lag_cor")

for (e in tables_to_export) {
  rio::export(get(e),
              file.path("excel_tables",
                        paste0(e, ".xlsx")))
}

## also export result from regression on lagged data 
rio::export(lag_mod, file.path("excel_tables", "lag_mod.rds"))

6 System information

6.1 Outline

The following information documents the system on which the document was compiled.

6.2 System

This provides information on the operating system.

Sys.info()
##                                                                                            sysname 
##                                                                                           "Darwin" 
##                                                                                            release 
##                                                                                           "19.5.0" 
##                                                                                            version 
## "Darwin Kernel Version 19.5.0: Tue May 26 20:41:44 PDT 2020; root:xnu-6153.121.2~2/RELEASE_X86_64" 
##                                                                                           nodename 
##                                                                                   "Mac-1830.local" 
##                                                                                            machine 
##                                                                                           "x86_64" 
##                                                                                              login 
##                                                                                             "root" 
##                                                                                               user 
##                                                                                           "runner" 
##                                                                                     effective_user 
##                                                                                           "runner"

6.3 R environment

This provides information on the version of R used:

R.version
##                _                           
## platform       x86_64-apple-darwin17.0     
## arch           x86_64                      
## os             darwin17.0                  
## system         x86_64, darwin17.0          
## status                                     
## major          4                           
## minor          0.2                         
## year           2020                        
## month          06                          
## day            22                          
## svn rev        78730                       
## language       R                           
## version.string R version 4.0.2 (2020-06-22)
## nickname       Taking Off Again

6.4 R packages

This provides information on the packages used:

sessionInfo()
## R version 4.0.2 (2020-06-22)
## Platform: x86_64-apple-darwin17.0 (64-bit)
## Running under: macOS Catalina 10.15.5
## 
## Matrix products: default
## BLAS:   /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRblas.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRlapack.dylib
## 
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] ggnewscale_0.4.1     ggpubr_0.4.0         lubridate_1.7.9     
##  [4] chngpt_2020.5-21     cyphr_1.1.0          DT_0.14             
##  [7] kableExtra_1.1.0     janitor_2.0.1        remotes_2.1.1       
## [10] projections_0.5.1    earlyR_0.0.1         epitrix_0.2.2       
## [13] distcrete_1.0.3      incidence_1.7.1      rio_0.5.16          
## [16] reshape2_1.4.4       rvest_0.3.5          xml2_1.3.2          
## [19] linelist_0.0.40.9000 forcats_0.5.0        stringr_1.4.0       
## [22] dplyr_1.0.0          purrr_0.3.4          readr_1.3.1         
## [25] tidyr_1.1.0          tibble_3.0.1         ggplot2_3.3.2       
## [28] tidyverse_1.3.0      here_0.1             reportfactory_0.0.5 
## 
## loaded via a namespace (and not attached):
##  [1] nlme_3.1-148      fs_1.4.2          webshot_0.5.2     httr_1.4.1       
##  [5] rprojroot_1.3-2   tools_4.0.2       backports_1.1.8   utf8_1.1.4       
##  [9] R6_2.4.1          mgcv_1.8-31       DBI_1.1.0         colorspace_1.4-1 
## [13] withr_2.2.0       gridExtra_2.3     tidyselect_1.1.0  sodium_1.1       
## [17] curl_4.3          compiler_4.0.2    cli_2.0.2         labeling_0.3     
## [21] matchmaker_0.1.1  scales_1.1.1      digest_0.6.25     foreign_0.8-80   
## [25] rmarkdown_2.3     pkgconfig_2.0.3   htmltools_0.5.0   dbplyr_1.4.4     
## [29] htmlwidgets_1.5.1 rlang_0.4.6       readxl_1.3.1      rstudioapi_0.11  
## [33] farver_2.0.3      generics_0.0.2    jsonlite_1.7.0    crosstalk_1.1.0.1
## [37] car_3.0-8         zip_2.0.4         kyotil_2019.11-22 magrittr_1.5     
## [41] Matrix_1.2-18     Rcpp_1.0.4.6      munsell_0.5.0     fansi_0.4.1      
## [45] viridis_0.5.1     abind_1.4-5       lifecycle_0.2.0   stringi_1.4.6    
## [49] yaml_2.2.1        carData_3.0-4     snakecase_0.11.0  MASS_7.3-51.6    
## [53] plyr_1.8.6        grid_4.0.2        blob_1.2.1        crayon_1.3.4     
## [57] lattice_0.20-41   cowplot_1.0.0     splines_4.0.2     haven_2.3.1      
## [61] hms_0.5.3         knitr_1.29        pillar_1.4.4      boot_1.3-25      
## [65] ggsignif_0.6.0    reprex_0.3.0      glue_1.4.1        evaluate_0.14    
## [69] data.table_1.12.8 modelr_0.1.8      vctrs_0.3.1       selectr_0.4-2    
## [73] cellranger_1.1.0  gtable_0.3.0      assertthat_0.2.1  xfun_0.15        
## [77] openxlsx_4.1.5    broom_0.5.6       rstatix_0.6.0     survival_3.1-12  
## [81] viridisLite_0.3.0 ellipsis_0.3.1